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Factorize the following algebraic expression,

$X^{3} - 23 x^{2} - 142 x + 120$

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(X - 1) (X - 6) (X - 12)

(X - 1) (X - 10) (X - 12)

(X - 5) (X + 8)

(X - 1) (X - 10) (X + 5)

answer is B.

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Detailed Solution

x 3 - 23 x 2 + 142 x - 120

= x 3 - x 2 - 22 x 2 + 22 x + 120 x - 120

= x 2 (x - 1) - 22 x (x - 1) + 120 (x - 1)

= (x - 1) (x 2 - 22 x + 120)

= (x - 1) [x 2 - 10 x - 12 x + 120]

= (x - 1) [x (x - 10) - 12 (x - 10)]

= (x - 1) (x - 10) (x - 12)

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